Abstract
A cooperative network model of sociological interest is examined to determine the sensitivity of the global dynamics to having a fraction of the members behaving uncooperatively, that is, being in conflict with the majority. We study a condition where in the absence of these uncooperative individuals, the contrarians, the control parameter exceeds a critical value and the network is frozen in a state of consensus. The network dynamics change with variations in the percentage of contrarians, resulting in a balance between the value of the control parameter and the percentage of those in conflict with the majority. We show that, as a finite-size effect, the transmission of information from a network B to a network A, with a small fraction of lookout members in A who adopt the behavior of B, becomes maximal when both networks are assigned the same critical percentage of contrarians.
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